Почему событие отметки времени в новом классе вызывает метод из form1 один раз, а в следующий раз он ничего не делает?

Вероятно, проблема заключается в том, что существует исключение, которое происходит где-то в вашем истекшем событии, и таймер никогда не запускается снова. Вы можете установить точку останова и следовать ей, чтобы в первый раз войти, чтобы увидеть, где/если она терпит неудачу. Кроме того, вы можете запрограммировать его, чтобы начать резервное копирование независимо:

static void _timer_Elapsed(object sender, ElapsedEventArgs e)
{
    _timer.Stop();

    try
    {
        LoadOldHtmlFiles();
        frm1.CombindedStringFix();
    }
    catch (Exception ex)
    {
        // do something (or nothing) with the exception
    }
    finally 
    {
        _timer.Start();
    }
}

Поскольку вы подтвердили, что происходит перекрестное потоковое исключение, я бы рекомендовал прочитать:

Как сделать безопасные вызовы для Windows Forms Controls

Вот их демо в случае, если ссылка когда-либо сломана:

using System;
using System.ComponentModel;
using System.Threading;
using System.Windows.Forms;

namespace CrossThreadDemo
{
    public class Form1 : Form
    {
        // This delegate enables asynchronous calls for setting 
        // the text property on a TextBox control. 
        delegate void SetTextCallback(string text);

        // This thread is used to demonstrate both thread-safe and 
        // unsafe ways to call a Windows Forms control. 
        private Thread demoThread = null;

        // This BackgroundWorker is used to demonstrate the  
        // preferred way of performing asynchronous operations. 
        private BackgroundWorker backgroundWorker1;

        private TextBox textBox1;
        private Button setTextUnsafeBtn;
        private Button setTextSafeBtn;
        private Button setTextBackgroundWorkerBtn;

        private System.ComponentModel.IContainer components = null;

        public Form1()
        {
            InitializeComponent();
        }

        protected override void Dispose(bool disposing)
        {
            if (disposing && (components != null))
            {
                components.Dispose();
            }
            base.Dispose(disposing);
        }

        // This event handler creates a thread that calls a  
        // Windows Forms control in an unsafe way. 
        private void setTextUnsafeBtn_Click(
            object sender, 
            EventArgs e)
        {
            this.demoThread = 
                new Thread(new ThreadStart(this.ThreadProcUnsafe));

            this.demoThread.Start();
        }

        // This method is executed on the worker thread and makes 
        // an unsafe call on the TextBox control. 
        private void ThreadProcUnsafe()
        {
            this.textBox1.Text = "This text was set unsafely.";
        }

        // This event handler creates a thread that calls a  
        // Windows Forms control in a thread-safe way. 
        private void setTextSafeBtn_Click(
            object sender, 
            EventArgs e)
        {
            this.demoThread = 
                new Thread(new ThreadStart(this.ThreadProcSafe));

            this.demoThread.Start();
        }

        // This method is executed on the worker thread and makes 
        // a thread-safe call on the TextBox control. 
        private void ThreadProcSafe()
        {
            this.SetText("This text was set safely.");
        }

        // This method demonstrates a pattern for making thread-safe 
        // calls on a Windows Forms control.  
        // 
        // If the calling thread is different from the thread that 
        // created the TextBox control, this method creates a 
        // SetTextCallback and calls itself asynchronously using the 
        // Invoke method. 
        // 
        // If the calling thread is the same as the thread that created 
        // the TextBox control, the Text property is set directly.  

        private void SetText(string text)
        {
            // InvokeRequired required compares the thread ID of the 
            // calling thread to the thread ID of the creating thread. 
            // If these threads are different, it returns true. 
            if (this.textBox1.InvokeRequired)
            {   
                SetTextCallback d = new SetTextCallback(SetText);
                this.Invoke(d, new object[] { text });
            }
            else
            {
                this.textBox1.Text = text;
            }
        }

        // This event handler starts the form  
        // BackgroundWorker by calling RunWorkerAsync. 
        // 
        // The Text property of the TextBox control is set 
        // when the BackgroundWorker raises the RunWorkerCompleted 
        // event. 
        private void setTextBackgroundWorkerBtn_Click(
            object sender, 
            EventArgs e)
        {
            this.backgroundWorker1.RunWorkerAsync();
        }

        // This event handler sets the Text property of the TextBox 
        // control. It is called on the thread that created the  
        // TextBox control, so the call is thread-safe. 
        // 
        // BackgroundWorker is the preferred way to perform asynchronous 
        // operations. 

        private void backgroundWorker1_RunWorkerCompleted(
            object sender, 
            RunWorkerCompletedEventArgs e)
        {
            this.textBox1.Text = 
                "This text was set safely by BackgroundWorker.";
        }

        #region Windows Form Designer generated code

        private void InitializeComponent()
        {
            this.textBox1 = new System.Windows.Forms.TextBox();
            this.setTextUnsafeBtn = new System.Windows.Forms.Button();
            this.setTextSafeBtn = new System.Windows.Forms.Button();
            this.setTextBackgroundWorkerBtn = new System.Windows.Forms.Button();
            this.backgroundWorker1 = new System.ComponentModel.BackgroundWorker();
            this.SuspendLayout();
            //  
            // textBox1 
            //  
            this.textBox1.Location = new System.Drawing.Point(12, 12);
            this.textBox1.Name = "textBox1";
            this.textBox1.Size = new System.Drawing.Size(240, 20);
            this.textBox1.TabIndex = 0;
            //  
            // setTextUnsafeBtn 
            //  
            this.setTextUnsafeBtn.Location = new System.Drawing.Point(15, 55);
            this.setTextUnsafeBtn.Name = "setTextUnsafeBtn";
            this.setTextUnsafeBtn.TabIndex = 1;
            this.setTextUnsafeBtn.Text = "Unsafe Call";
            this.setTextUnsafeBtn.Click += new System.EventHandler(this.setTextUnsafeBtn_Click);
            //  
            // setTextSafeBtn 
            //  
            this.setTextSafeBtn.Location = new System.Drawing.Point(96, 55);
            this.setTextSafeBtn.Name = "setTextSafeBtn";
            this.setTextSafeBtn.TabIndex = 2;
            this.setTextSafeBtn.Text = "Safe Call";
            this.setTextSafeBtn.Click += new System.EventHandler(this.setTextSafeBtn_Click);
            //  
            // setTextBackgroundWorkerBtn 
            //  
            this.setTextBackgroundWorkerBtn.Location = new System.Drawing.Point(177, 55);
            this.setTextBackgroundWorkerBtn.Name = "setTextBackgroundWorkerBtn";
            this.setTextBackgroundWorkerBtn.TabIndex = 3;
            this.setTextBackgroundWorkerBtn.Text = "Safe BW Call";
            this.setTextBackgroundWorkerBtn.Click += new System.EventHandler(this.setTextBackgroundWorkerBtn_Click);
            //  
            // backgroundWorker1 
            //  
            this.backgroundWorker1.RunWorkerCompleted += new System.ComponentModel.RunWorkerCompletedEventHandler(this.backgroundWorker1_RunWorkerCompleted);
            //  
            // Form1 
            //  
            this.ClientSize = new System.Drawing.Size(268, 96);
            this.Controls.Add(this.setTextBackgroundWorkerBtn);
            this.Controls.Add(this.setTextSafeBtn);
            this.Controls.Add(this.setTextUnsafeBtn);
            this.Controls.Add(this.textBox1);
            this.Name = "Form1";
            this.Text = "Form1";
            this.ResumeLayout(false);
            this.PerformLayout();

        }

        #endregion


        [STAThread]
        static void Main()
        {
            Application.EnableVisualStyles();
            Application.Run(new Form1());
        }

    }
}